Question: Solve for $x$ and $y$ using substitution. ${x+y = 4}$ ${y = -5x-8}$
Solution: Since $y$ has already been solved for, substitute $-5x-8$ for $y$ in the first equation. ${x + }{(-5x-8)}{= 4}$ Simplify and solve for $x$ $x-5x - 8 = 4$ $-4x-8 = 4$ $-4x-8{+8} = 4{+8}$ $-4x = 12$ $\dfrac{-4x}{{-4}} = \dfrac{12}{{-4}}$ ${x = -3}$ Now that you know ${x = -3}$ , plug it back into $\thinspace {y = -5x-8}\thinspace$ to find $y$ ${y = -5}{(-3)}{ - 8}$ $y = 15 - 8$ $y = 7$ You can also plug ${x = -3}$ into $\thinspace {x+y = 4}\thinspace$ and get the same answer for $y$ : ${(-3)}{ + y = 4}$ ${y = 7}$